A linear frequency-domain model of a static VAr compensator (STATCOM) is presented. Large signal transfers are derived to determine characteristic harmonics, and small-signal transfers are derived to determine noncharacteristic harmonics. Harmonic transfers are also derived for phase-locked loop and reactive power controls, and the response of a controlled STATCOM to a negative sequence fundamental frequency imbalance is demonstrated. As the model is linear, it is very computationally efficient, and is well suited to analysis of large networks with a number of similar connected FACTs devices. The importance of including full control dynamics for harmonic analysis is also clearly shown.